The von Neumann/Morgenstern approach to ambiguity
A choice problem is risky (respectively ambiguous) if the decision maker is choosing between probability distributions (respectively sets of probability distributions) over utility relevant consequences. We provide an axiomatic foundation for and a representation of continuous linear preferences over sets of probabilities on consequences. The representation theory delivers: first and second order dominance for ambiguous problems; a utility interval based dominance relation that distinguishes between sources of uncertainty; a complete theory of updating convex sets of priors; a Bayesian theory of the value of ambiguous information structures; complete separations of attitudes toward risk and ambiguity; and new classes of preferences that allow decreasing relative ambiguity aversion and thereby rationalize recent challenges to many of the extant multiple prior models of ambiguity aversion. We also characterize a property of sets of priors, descriptive completeness, that resolves several open problems and allows multiple prior models to model as large a class of problems as the continuous linear preferences presented here.
|Date of creation:||May 2013|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.imw.uni-bielefeld.de/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Amarante, Massimiliano, 2009. "Foundations of neo-Bayesian statistics," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2146-2173, September.
- Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
- Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February.
- Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011.
"Rational preferences under ambiguity,"
Springer, vol. 48(2), pages 341-375, October.
- Marciano Siniscalchi, 2003.
"A Behavioral Characterization of Plausible Priors,"
1365, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Thibault Gajdos & Takashi Hayashi & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2006.
"Attitude toward imprecise information,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
- Thibault Gajdos & Takashi Hayashi & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2006. "Attitude toward imprecise information," Cahiers de la Maison des Sciences Economiques v06081, Université Panthéon-Sorbonne (Paris 1).
- Thibault Gajdos & Takashi Hayashi & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2008. "Attitude toward imprecise information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00451982, HAL.
- Sujoy Mukerji & Peter Klibanoff, 2002.
"A Smooth Model of Decision,Making Under Ambiguity,"
Economics Series Working Papers
113, University of Oxford, Department of Economics.
- Larry G. Epstein & Jiankang Zhang, 1999.
"Subjective Probabilities on Subjectively Unambiguous Events,"
Carleton Economic Papers
99-18, Carleton University, Department of Economics.
- Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
- Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
- David Schmeidler, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Levine's Working Paper Archive
7662, David K. Levine.
- Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
- AMARANTE, Massimiliano, 2009.
"Analogy in Decision-Making,"
Cahiers de recherche
14-2009, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-59, July.
- David S. Ahn, 2008. "Ambiguity Without a State Space," Review of Economic Studies, Oxford University Press, vol. 75(1), pages 3-28.
- Chew, Soo Hong & Epstein, Larry G. & Zilcha, Itzhak, 1988. "A correspondence theorem between expected utility and smooth utility," Journal of Economic Theory, Elsevier, vol. 46(1), pages 186-193, October.
- Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
- Fang, Fang & Stinchcombe, Maxwell B. & Whinston, Andrew B., 2010. "Proper scoring rules with arbitrary value functions," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1200-1210, November.
- Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004.
"Ambiguity Aversion, Robustness, and the Variational Representation of Preferences,"
Carlo Alberto Notebooks
12, Collegio Carlo Alberto, revised 2006.
- Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
- Maxwell B. Stinchcombe, 1994.
"Countably Additive Subjective Probabilities,"
CARE Working Papers
9403, The University of Texas at Austin, Center for Applied Research in Economics.
- Stigler, George J & Becker, Gary S, 1977. "De Gustibus Non Est Disputandum," American Economic Review, American Economic Association, vol. 67(2), pages 76-90, March.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
When requesting a correction, please mention this item's handle: RePEc:bie:wpaper:480. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dr. Frederik Herzberg)
If references are entirely missing, you can add them using this form.